OFFSET
1,1
COMMENTS
Cletus Emmanuel calls these "Kynea numbers".
Difference between the smallest digitally balanced number with 2n+4 binary digits and the largest digitally balanced number with 2n+2 binary digits (see A031443): 7 = 9-2 = 1001-10, 23 = 35-12 = 100011-1100, 79 = 135-56 = 10000111-111000 etc. - Juri-Stepan Gerasimov, Jun 01 2011
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1660
Amelia Carolina Sparavigna, Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers(Carol and Kynea Numbers), Department of Applied Science and Technology, Politecnico di Torino (Italy, 2019).
Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
Eric Weisstein's World of Mathematics, Near-Square Prime
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
a(n) = 4^n+2^(n+1)-1.
G.f.: -x*(7-26*x+16*x^2) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Jun 01 2011
E.g.f.: -exp(x) + 2*exp(2*x) + exp(4*x) - 2. - Stefano Spezia, Dec 09 2019
EXAMPLE
G.f. = 7*x + 23*x^2 + 79*x^3 + 287*x^4 + 1087*x^5 + 4223*x^6 + 16639*x^7 + ...
MATHEMATICA
a[ n_] := If[ n < 1, 0, 4^n + 2^(n + 1) - 1]; (* Michael Somos, Jul 08 2014 *)
CoefficientList[Series[(7 - 26*x + 16*x^2)/((1 - x)*(2*x - 1)*(4*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 08 2014 *)
PROG
(PARI) vector(100, n, (2^n+1)^2-2) \\ Colin Barker, Jul 08 2014
(PARI) Vec(-(16*x^2-26*x+7)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 08 2014
(Magma) [(2^n+1)^2-2 : n in [1..30]]; // Wesley Ivan Hurt, Jul 08 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 17 2004
EXTENSIONS
More terms from Colin Barker, Jul 08 2014
STATUS
approved